Polytope of Type {12,15} with group SmallGroup(1440,4642)

Overview

Group: SmallGroup(1440,4642)
Rank: 3
Schläfli Type: {12,15}
Vertices, edges, …: 48, 360, 60
Order of s₀s₁s₂: 20
Order of s₀s₁s₂s₁: 60
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Orientable

Quotients maximal quotients in bold

2-fold

{6,15}*720c

3-fold

{12,5}*480

4-fold

{3,15}*360

6-fold

{6,5}*240b

12-fold

24-fold

{3,5}*60

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := ( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)(50,51);;
s1 := ( 1, 5)( 2,22)( 3,21)( 4,23)( 6,13)( 7,19)( 8,45)( 9,43)(10,46)(11,27)(12,24)(14,25)(15,48)(16,40)(17,36)(18,44)(20,35)(26,37)(28,34)(29,31)(30,39)(32,47)(33,38)(41,42)(49,50);;
s2 := ( 1,12)( 2,29)( 3,21)( 4,31)( 5,13)( 6,46)( 7,36)( 8,45)( 9,27)(10,42)(11,38)(14,44)(15,28)(16,48)(17,40)(18,23)(19,34)(20,35)(22,25)(24,41)(26,43)(30,39)(32,37)(33,47)(50,51);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(51)!( 2,39)( 3,43)( 5,45)( 6, 7)( 8,13)( 9,22)(10,18)(11,41)(14,16)(17,33)(19,20)(21,26)(23,42)(24,38)(25,27)(29,30)(34,35)(36,46)(40,47)(44,48)(50,51);
s1 := Sym(51)!( 1, 5)( 2,22)( 3,21)( 4,23)( 6,13)( 7,19)( 8,45)( 9,43)(10,46)(11,27)(12,24)(14,25)(15,48)(16,40)(17,36)(18,44)(20,35)(26,37)(28,34)(29,31)(30,39)(32,47)(33,38)(41,42)(49,50);
s2 := Sym(51)!( 1,12)( 2,29)( 3,21)( 4,31)( 5,13)( 6,46)( 7,36)( 8,45)( 9,27)(10,42)(11,38)(14,44)(15,28)(16,48)(17,40)(18,23)(19,34)(20,35)(22,25)(24,41)(26,43)(30,39)(32,37)(33,47)(50,51);
poly := sub<Sym(51)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References